Keywords: Local mean decomposition Data fusion Complex signal analysis Time–frequency analysis Signal nonlinearity Spike identification a b s t r a c t The local mean decomposition (LMD) has been recently developed for the analysis of time series which have nonlinearity and nonstationarity. The smoothed local mean of the LMD surpasses the cubic spline method used by the empirical mode decomposi...

Intra-pulse modulation recognition under negative signal-to-noise ratio (SNR) environment is a research challenge. This article presents a robust algorithm for the recognition of 5 types of radar signals with large variation range in the signal parameters in low SNR using the combination of the Short-time Ramanujan Fourier transform (ST-RFT) and pseudo-Zernike moments invariant features. The ST...

We derive a Riemann--Hilbert representation for the solution of an integrable nonlinear evolution equation with $3 \times 3$ Lax pair. use derived to obtain formulas long-time asymptotics.

In signal processing, Hilbert transform is used as an analytical tool. Hilbert Transform (HT) is useful in certain kinds of modulation schemes and also for bounded signals. The overall narrow band signals can be easily interpreted in terms of amplitude and frequency modulation. The various applications are present in magnetic recording, filter designing, edge detection and image processing. Key...

In this expository paper we present an overview of various graphical categorifications of the Heisenberg algebra and its Fock space representation. We begin with a discussion of “weak” categorifications via modules for Hecke algebras and “geometrizations” in terms of the cohomology of the Hilbert scheme of points on the resolution of a simple singularity. We then turn our attention to more rece...

We present a unified representation theorem for the Drazin inverse of linear operators in Hilbert space and a general error bound. Five specific expressions, computational procedures, and their error bounds for the Drazin inverse are uniformly derived from the unified representation theorem. 2002 Elsevier Science Inc. All rights reserved.

A variational representation for positive functionals of a Hilbert space valued Wiener process (W (·)) is proved. This representation is then used to prove a large deviations principle for the family {G (W (·))} >0 where G is an appropriate family of measurable maps from the Wiener space to some Polish space.

We present a constructive proof of the Stone-Yosida representation theorem for Riesz spaces motivated by considerations from formal topology. This theorem is used to derive a representation theorem for f-algebras. In turn, this theorem implies the Gelfand representation theorem for C*-algebras of operators on Hilbert spaces as formulated by Bishop and Bridges. Our proof is shorter, clearer, and...

A number of wave energy controllers tune the power take-off (PTO) system to the frequency of incident waves. Since real ocean waves are non-stationary by nature and not defined by a single frequency component, the PTO can be either tuned at a constant frequency characterized by the local spectrum, or continuously tuned to a representative wave frequency. In either case, a time-frequency represe...

Characterization of the *-subalgebras in the algebra of bounded operators acting on Hilbert space is presented. Sufficient conditions for the existence of a faithful representation in pre-Hilbert space of a *-algebra in terms of its Groebner basis are given. These conditions are generalization of the unshrinkability of monomial *-algebras introduced by C. Lance and P. Tapper. The applications t...